Vulkan gives all the tools to avoid any "lag spikes" from shader compiling. In fact, causing them is much more difficult than OpenGL where they could happen in surprising places (and only on certain hardware).
The issue is two fold: 1. Some engines produce a lot of shader permutations. Some AAA titles can have 60000 different shaders compiled. 2. Some GPU rasterizer states (such as color blending) are implemented as shader epilogues.
In Vulkan 1.0 almost all of the pipeline state had to be pre-baked into a pipeline state object compiled ahead of time. This lead to a "shader permutation explosion" where different states need different pipelines.
This requires the game engine to either a) compile all the pipeline combinations ahead of time (slow loading time) or b) compile them as needed (lag spikes).
The core issue for this was solved years ago and now most of the pipeline states can be added to the command buffers ("dynamic states"). This solves the permutation explosion. But at the same time it opens the door for issue 2: some states (blending in particular) can cause a state-based recompile (like ye olde OpenGL days) at runtime.
The only solution to the second problem is not to use the dynamic states that trigger recompiling. That's basically only blending as far as I know. You can't even have dynamic blend state on all GPUs.
For maximum developer flexibility there's the shader object extension that allows mixing and matching shaders and pipeline states any way you want. This will cause state based recompiles at unpredictable times but it's an opt-in feature and easy to avoid if lag spikes are not wanted.
tl;dr: shader recompilation is easy to avoid in Vulkan but porting legacy engine code or art content may take you off the happy path.
For Vulkan you already ship "pre-compiled" shaders in SPIR-V form. The SPIR-V needs to be compiled to GPU ISA before it can run.
You can't, in general, pre-compile the SPIR-V to GPU ISA because you don't know the target device you're running on until the app launches. You would have to precompile ISA for every GPU you ever plan to run on, for every platform, for every driver version they've ever released that you will run on. Also you need to know when new hardware and drivers come out and have pre-compiled ISA ready for them.
Steam tries to do this. They store pre-compiled ISA tagged with the GPU+Driver+Platform, then ship it to you. Kinda works if they have the shaders for a game compiled for your GPU/Driver/Platform. In reality your cache hit rate will be spotty and plenty of people are going to stutter.
OpenGL/DirectX11 still has this problem too, but it's all hidden in the driver. Drivers would do a lot of heroics to hide compilation stutter. They'd still often fail though and developers had no way to really manage it out outside of some truly disgusting hacks.
But in reality the exhaustive pre-compile will compile way more than will be used by any given game session (on average) and waste lots of time. Also you would have to recompile every time the user upgraded their driver version or changed hardware. And you're likely to churn a lot of customers if you smack them with a 30+ minute loading screen.
Precisely which shaders get used by the game can only be correctly discovered at runtime in many games, it depends on the precise state of the game/renderer and the quality settings and often hardware vendor if there are vendor-specific code paths.
Some games will get QA to play a bunch of the game, or maybe setup automated scripts to fly through all the levels and log which shaders get used. Then that log gets replayed in a startup pre-compile loading screen so you're at least pre-compiling shaders you know will be used.
Steam could improve the experience here by having the shaders compile overnight in the background so it presents zero delay but the current way doesn't bother me much at all.
Really depends on the game.
There's no easy way around this problem. It never came up as much in the OpenGL/D3D11 era because we didn't make as many shaders back then. Shader graphs and letting artists author shaders really opened pandoras box on this problem, but OpenGL was already on its way out by the time these techniques were proliferating so Vulkan gets lumped in as the cause.